Who’s who in networks. Wanted: the key player. (English) Zbl 1138.91590

Ballester, Coralio; Calvó-Armengol, Antoni; Zenou, Yves

Econometrica 74, No. 5, 1403-1417 (2006).

Summary: Finite population noncooperative games with linear-quadratic utilities, where each player decides how much action she exerts, can be interpreted as a network game with local payoff complementarities, together with a globally uniform payoff substitutability component and an own-concavity effect. For these games, the Nash equilibrium action of each player is proportional to her Bonacich centrality in the network of local complementarities, thus establishing a bridge with the sociology literature on social networks. This Bonacich-Nash linkage implies that aggregate equilibrium increases with network size and density. We then analyze a policy that consists of targeting the key player, that is, the player who, once removed, leads to the optimal change in aggregate activity. We provide a geometric characterization of the key player identified with an intercentrality measure, which takes into account both a player’s centrality and her contribution to the centrality of the others.

MSC:

91D30	Social networks; opinion dynamics
91A43	Games involving graphs

Keywords:

social networks; peer effects; centrality measures; policies